Suppose x is a positive even number, all of whose digits

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Gmat_mission: Legendary Member; Posts: 1622; Joined: Thu Mar 01, 2018 7:22 am; Followed by:2 members

Suppose x is a positive even number, all of whose digits

by Gmat_mission » Sun Jun 30, 2019 9:22 am

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Suppose x is a positive even number, all of whose digits are either 3 or 4. If x is also divisible by both 3 and 4, how many digits are in the smallest possible value of x?

A. Three
B. Four
C. Five
D. Six
E. Seven

[spoiler]OA=A[/spoiler]

Source: Veritas Prep

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Source: Beat The GMAT — Problem Solving | Sun Jun 30, 2019 9:22 am

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Ian Stewart: GMAT Instructor; Posts: 2623; Joined: Mon Jun 02, 2008 3:17 am; Location: Montreal; Thanked: 1090 times; Followed by:355 members; GMAT Score:780

by Ian Stewart » Mon Jul 01, 2019 6:34 am

If the number is even, and its digits are all 3s and 4s, it must end in 4. If the number is divisible by 4, its last two digits must form a multiple of 4, so must be "44" (and not "34"). If the number is divisible by 3, the sum of its digits is a multiple of 3, and we can see that "444" satisfies all of the criteria in the question, so A is the answer.

Though I think a test taker could justifiably assume, from the question's wording, that the number should contain at least one digit that is a "3", and at least one digit that is a "4". Under that assumption, the answer would be "four", since 3444 satisfies all of the conditions.

For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8086; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

by Scott@TargetTestPrep » Tue Jul 02, 2019 5:43 pm

Gmat_mission wrote:Suppose x is a positive even number, all of whose digits are either 3 or 4. If x is also divisible by both 3 and 4, how many digits are in the smallest possible value of x?

A. Three
B. Four
C. Five
D. Six
E. Seven

[spoiler]OA=A[/spoiler]

Source: Veritas Prep

To be divisible by 4, the final two digits of the number must be divisible by 4; to be divisible by 3, the sum of all the digits of the number must be divisible by 3. The smallest number that is divisible by 3 and 4 with digits of 3 and/or 4 is 444. So it has three digits.

Answer: A

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